Solving Systems with Cramer's Rule · Exercise 66

Use this scenario: A health-conscious company decides to make a trail mix out of almonds, dried cranberries, and chocolate-covered cashews. The nutritional information for these items is shown in the table.
$$\begin{array}{cccc}& \text{Fat (g)}& \text{Protein (g)}& \text{Carbohydrates (g)}\\ \text{Almonds (10)}& \text{6}& \text{2}& \text{3}\\ \text{Cranberries (10)}& \text{0.02}& \text{0}& \text{8}\\ \text{Cashews (10)}& \text{7}& \text{3.5}& \text{5.5}\end{array}$$

For the special “low-carb”trail mix, there are 1,000 pieces of mix. The total number of carbohydrates is 425 g, and the total amount of fat is 570.2 g. If there are 200 more pieces of cashews than cranberries, how many of each item is in the trail mix?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §11.8 Solving Systems with Cramer's Rule · Exercise 66